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Topology of groups of automorphisms of surfaces, and high dimensional analogues.

6 votes
2 answers
507 views

generators for the handlebody group of genus two

Is the handlebody group of genus two surface generated by Dehn twists along properly embedded disks and annuli? Are there alternative ways to describe a set of generators that are conceptually simple …
5 votes
2 answers
521 views

Finiteness properties of mapping class groups

Question: Is it known if the mapping class groups (of surfaces of finite type) are similar to Gromov-hyperbolic groups in the following senses: 1) Does every finite generating set give us a finite p …
2 votes
1 answer
181 views

index of the subgroup of the mapping class group acting trivially on Z/3Z homology

Let $S=S_g$ be the closed orientable surface of genus $g$ and let $\Gamma_3(S)$ be the subgroup of the mapping class group, $Mod(S)$, which acts trivially on $H_1(S;\mathbb{Z/3\mathbb{Z}})$. Define $\ …